Sums payable by exactly n banknotes.

[zak seidov]

Dear Neil, seqfans,

1) can anyone check/extend these figures?
2) what about case n => inf?
3) is this worth submitting?

thanks, zak


%N A1 Number of sums payable by exactly n banknotes of
nominals 1,5,10,20,50,100.

%S A1 6, 15, 52, 103, 174, 262, 360, 461, 561, 660.

%e A1
n=1: 6 payable sums are 1,5,10,20,50,100;
n=2: 15 sums are 2,6,10,11,15,20,21,25,30,40,51,
55,60,70,100;
n=3: 52 sums are in A135137;
n=4: 103 sums are:
4,8,12,13,16,17,20,21,22,23,25,26,27,30,31,32,35,36,40,41,42,45,46,50,51,53,55,57,60,61,62,65,66,70,71,72,75,76,80,81,85,90,91,95,100,102,103,106,107,110,111,112,115,116,120,121,122,125,126,130,131,135,140,141,145,150,151,152,155,156,160,161,165,170,171,175,180,190,200,201,202,205,206,210,211,215,220,221,225,230,240,250,251,255,260,270,300,301,305,310,320,350,400.
  


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zs> From seqfan-owner at ext.jussieu.fr  Fri Feb 15 13:30:08 2008
zs> Date: Fri, 15 Feb 2008 04:29:51 -0800 (PST)
zs> From: zak seidov <zakseidov at yahoo.com>
zs> Subject: A135045: missed terms(?)
zs> To: njas at research.att.com, mvaldivia at ugr.es, seqfan at ext.jussieu.fr
zs> ...
zs> 
zs> Neil, Manuel. seqfans,
zs> 
zs> there are some missed terms in A135045.
zs> 
zs> Sequence begins:
zs> 
zs> 10,13,16,17,20,23,24,26,29,30,32,35,38,41,44,47,48,50,57,64,65,68,70,73,80,82,83,94,95
zs> 
zs> Better someone check these independently.

Problem solved: Manuel has informed Zak on the actual definition of A135045
and will submit a correction: The "24, 30, 68, 268, 434, 520" are

%N A135045 Numbers in A001043 which are the sum of two terms of A001043 in one way.
%C Subset of A134651. No further term between 520 and 650000. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 16 2008

Richard